# Modeling Complex Living Systems

Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)

Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)

Using tools from mathematical kinetic theory and stochastic game theory, this work deals with the modeling of large complex systems in the applied sciences, particularly those comprised of several interacting individuals whose dynamics follow rules determined by some organized, or even "intelligent" ability. Traditionally, methods of mathematical kinetic theory have been applied to model the evolution of large systems of interacting classical or quantum particles. This book, on the other hand, examines the modeling of living systems as opposed to inert systems.

The author develops new mathematical methods and tools—hopefully a "new" mathematics—toward the modeling of living systems. Such tools need to be far more complex than those dealing with systems of inert matter. The first part of the book deals with deriving general evolution equations that can be customized to particular systems of interest in the applied sciences. The second part of the book deals with various models and applications.

The presentation unfolds using the following common approach in each chapter:

* Phenomenological interpretation of the physical system in the context of mathematical modeling

* Derivation of the mathematical model using methods from mathematical kinetic theory for active particles

* Simulations, parameter sensitivity analysis, and critical inspection of the derived model towards validation

* Overview of presented ideas to improve existing models, with special emphasis on applications

Specific topics covered include:

* Modeling of the competition between cells of an aggressive invasive agent and cells of the immune system

* Modeling of vehicular traffic flow

* Modeling of swarms and crowd dynamics in complex geometric environments

* Methodological aspects related to multiscale modeling of large systems viewed as interconnected subsystems

**Modeling Complex Living Systems** is a valuable resource for applied mathematicians, engineers, physicists, biologists, economists, and graduate students involved in modeling complex social systems and living matter in general.

Simulation complex living systems complex systems game theory immune system competition mathematical kinetic theory mathematical modeling model modeling multiscale and mini-structure modeling stochastic game theory swarms and crowd dynamics system modeling vehicular traffic flow

- DOI https://doi.org/10.1007/978-0-8176-4600-4
- Copyright Information Birkhäuser Boston 2008
- Publisher Name Birkhäuser Boston
- eBook Packages Mathematics and Statistics
- Print ISBN 978-0-8176-4510-6
- Online ISBN 978-0-8176-4600-4
- Series Print ISSN 2164-3679
- Series Online ISSN 2164-3725
- About this book